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A331037 Numbers k such that the sum of the divisors of k (except for 1 and k) plus the sum of the digits of k is equal to k. 2
1, 2, 3, 5, 7, 14, 52, 76, 2528, 9536, 9664, 35456, 138496, 8456192, 33665024, 33673216, 537444352, 2148958208, 137454419968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Additional terms include 537444352, 2148958208, 137454419968, 35184644718592, 9007202811510784. Are there any terms > 1 not of the form 2^k*p where p is prime and k>0? - David A. Corneth, Jan 08 2020

Terms not of the form 2^k*p do exist, for example 2^15*65713*24194197 and 2^19*1739719*2639431. - Giovanni Resta, Jan 08 2020

a(20) > 10^13. - Giovanni Resta, Jan 14 2020

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

The first term that is not 1 or a single-digit prime is obtained by adding the proper divisors of 14 other than 1 (2,7) to its digits (1,4): (2+7) + (1+4) = 14.

The second such term is 52: the proper divisors of 52 other than 1 (2,4,13,26) and its digits (5,2) sum to (2+4+13+26) + (5+2) = 52.

MATHEMATICA

Select[Range[10^7], DivisorSigma[1, #] - # - If[# == 1, 0, 1] + Plus @@ IntegerDigits[#] == # &] (* Amiram Eldar, Jan 12 2020 *)

PROG

(PARI) is(n) = n == sigma(n)-1-if(n>1, n, 0)+sumdigits(n) \\ Rémy Sigrist, Jan 08 2020

CROSSREFS

Cf. A000203, A007953, A048050.

Cf. A331093 (sum of divisors - digit sum = the number).

Sequence in context: A324840 A316475 A303875 * A228652 A157833 A175758

Adjacent sequences:  A331034 A331035 A331036 * A331038 A331039 A331040

KEYWORD

nonn,base,more,less

AUTHOR

Joseph E. Marrow, Jan 08 2020

EXTENSIONS

a(14)-a(16) from Rémy Sigrist, Jan 08 2020

a(17)-a(19) from Giovanni Resta, Jan 14 2020

STATUS

approved

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Last modified February 17 21:46 EST 2020. Contains 332006 sequences. (Running on oeis4.)